$\ce{CO2}$ gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of $\ce{CO2}$ adsorbed becomes 64 times when the pressure of $\ce{CO2}$ is doubled. The value of $n$ in the Freundlich isotherm equation is ______ $\times 10^{-2}$. (Round off to the Nearest integer)

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Surface Chemistry

CO X_{2}

gas adsorbs on charcoal following Freundlich adsorption isotherm. For a given amount of charcoal, the mass of

CO X_{2}

adsorbed becomes 64 times when the pressure of

CO X_{2}

is doubled. The value of

n

in the Freundlich isotherm equation is ______

\times 1 0^{- 2}

.
(Round off to the Nearest integer)

Answer: 17

The Freundlich adsorption isotherm is

\frac{x}{m} = k P^{1/ n}

Writing it at the two pressures and dividing one by the other,

\frac{( x / m ) _{2}}{( x / m ) _{1}} = (\frac{2 P}{P})^{1/ n} = 2^{1/ n}

The adsorbed mass becomes

64

times, so

2^{1/ n} = 64 = 2^{6} \Rightarrow \frac{1}{n} = 6

n = \frac{1}{6} = 0.1667 = 16.67 \times 1 0^{- 2}

Rounded to the nearest integer, the value required is

17

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Integer answer